Let the mean and the variance of 20 observations x₁, x₂,, x₂₀ be 15 and 9, respectively. For α R, if the mean of (x₁+α)²,(x₂+α)²,,(x₂₀+α)² is 178, then the square of the maximum value of α is equal to _ _ _ _.

Statistics and Probability: JEE Main 2022 Mathematics question

JEE Main 2022 · 29 Jul, Morning shift · Q47

JEE Main 202229 Jul, Morning shiftMathematicsMediumStatistics and Probability258× since 2002

Let the mean and the variance of 20 observations

x_{1}, x_{2}, \ldots, x_{20}

be 15 and 9 , respectively. For

\alpha \in \mathbf{R}

, if the mean of

\left(x_{1}+\alpha\right)^{2},\left(x_{2}+\alpha\right)^{2}, \ldots,\left(x_{20}+\alpha\right)^{2}

is 178 , then the square of the maximum value of

\alpha

is equal to ________.

Your answerType your answer. Integers and decimals are accepted.